Nadia is 4 times as old as Christopher. Six years ago, Nadia was 7 times as old as Christopher. How old is Nadia now?
Answer: We can use the given information to write down two equations that describe the ages of Nadia and Christopher. Let Nadia's current age be $n$ and Christopher's current age be $c$ The information in the first sentence can be expressed in the following equation: $n = 4c$ Six years ago, Nadia was $n - 6$ years old, and Christopher was $c - 6$ years old. The information in the second sentence can be expressed in the following equation: $n - 6 = 7(c - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $n$ , it might be easiest to solve our first equation for $c$ and substitute it into our second equation. Solving our first equation for $c$ , we get: $c = n / 4$ . Substituting this into our second equation, we get: $n - 6 = 7($ $(n / 4)$ $- 6)$ which combines the information about $n$ from both of our original equations. Simplifying the right side of this equation, we get: $n - 6 = \dfrac{7}{4} n - 42$ Solving for $n$ , we get: $\dfrac{3}{4} n = 36$ $n = \dfrac{4}{3} \cdot 36 = 48$.